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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/systems_of_equations/systems_of_equations_ex3" target="_blank">Open systems_of_equations_ex3 in new tab.</a>
<a name="output"></a> 
<br><br><br> <h1> The console output of the program: </h1> 
<pre>
***************************************************************
* Running Example systems_of_equations_ex3:
*   example-opt  
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=1681
    n_local_nodes()=1681
  n_elem()=400
    n_local_elem()=400
    n_active_elem()=400
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "Navier-Stokes"
    Type "TransientLinearImplicit"
    Variables={ "u" "v" } "p" "alpha" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" "LAGRANGE", "JACOBI_20_00" "SCALAR", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" "CARTESIAN" "CARTESIAN" 
    Approximation Orders="SECOND", "THIRD" "FIRST", "THIRD" "FIRST", "THIRD" 
    n_dofs()=3804
    n_local_dofs()=3804
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=3
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 40.9611
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 3804
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0



*** Solving time step 0, time = 0.01 ***
Linear solver converged at step: 51, final residual: 0.000282517  Nonlinear convergence: ||u - u_old|| = 351.27
Linear solver converged at step: 28, final residual: 1.94309e-05  Nonlinear convergence: ||u - u_old|| = 0.669457
Linear solver converged at step: 26, final residual: 9.95896e-08  Nonlinear convergence: ||u - u_old|| = 0.00106343
Linear solver converged at step: 51, final residual: 2.26529e-12  Nonlinear convergence: ||u - u_old|| = 1.31622e-06
 Nonlinear solver converged at step 3


*** Solving time step 1, time = 0.02 ***
Linear solver converged at step: 43, final residual: 0.000268558  Nonlinear convergence: ||u - u_old|| = 28.9406
Linear solver converged at step: 22, final residual: 2.0417e-05  Nonlinear convergence: ||u - u_old|| = 0.0406665
Linear solver converged at step: 24, final residual: 1.12851e-07  Nonlinear convergence: ||u - u_old|| = 0.000315505
 Nonlinear solver converged at step 2


*** Solving time step 2, time = 0.03 ***
Linear solver converged at step: 37, final residual: 0.000211074  Nonlinear convergence: ||u - u_old|| = 5.51321
Linear solver converged at step: 22, final residual: 1.01234e-05  Nonlinear convergence: ||u - u_old|| = 0.0101518
Linear solver converged at step: 27, final residual: 2.18784e-08  Nonlinear convergence: ||u - u_old|| = 8.18272e-05
 Nonlinear solver converged at step 2


*** Solving time step 3, time = 0.04 ***
Linear solver converged at step: 28, final residual: 0.000239353  Nonlinear convergence: ||u - u_old|| = 1.98648
Linear solver converged at step: 18, final residual: 1.38776e-05  Nonlinear convergence: ||u - u_old|| = 0.00606589
Linear solver converged at step: 26, final residual: 3.41727e-08  Nonlinear convergence: ||u - u_old|| = 0.000775948
 Nonlinear solver converged at step 2


*** Solving time step 4, time = 0.05 ***
Linear solver converged at step: 23, final residual: 0.000270828  Nonlinear convergence: ||u - u_old|| = 0.903052
Linear solver converged at step: 19, final residual: 2.04306e-05  Nonlinear convergence: ||u - u_old|| = 0.0091482
Linear solver converged at step: 24, final residual: 1.26651e-07  Nonlinear convergence: ||u - u_old|| = 0.000229152
 Nonlinear solver converged at step 2


*** Solving time step 5, time = 0.06 ***
Linear solver converged at step: 23, final residual: 0.000286865  Nonlinear convergence: ||u - u_old|| = 0.465778
Linear solver converged at step: 15, final residual: 2.34656e-05  Nonlinear convergence: ||u - u_old|| = 0.00318115
Linear solver converged at step: 22, final residual: 1.43996e-07  Nonlinear convergence: ||u - u_old|| = 0.000212093
 Nonlinear solver converged at step 2


*** Solving time step 6, time = 0.07 ***
Linear solver converged at step: 20, final residual: 0.000215688  Nonlinear convergence: ||u - u_old|| = 0.257386
Linear solver converged at step: 18, final residual: 9.85097e-06  Nonlinear convergence: ||u - u_old|| = 0.00379004
Linear solver converged at step: 28, final residual: 1.86885e-08  Nonlinear convergence: ||u - u_old|| = 0.000111296
 Nonlinear solver converged at step 2


*** Solving time step 7, time = 0.08 ***
Linear solver converged at step: 16, final residual: 0.000286567  Nonlinear convergence: ||u - u_old|| = 0.147885
Linear solver converged at step: 17, final residual: 1.39735e-05  Nonlinear convergence: ||u - u_old|| = 0.00297817
Linear solver converged at step: 28, final residual: 2.81987e-08  Nonlinear convergence: ||u - u_old|| = 0.000639703
 Nonlinear solver converged at step 2


*** Solving time step 8, time = 0.09 ***
Linear solver converged at step: 12, final residual: 0.000267583  Nonlinear convergence: ||u - u_old|| = 0.0836533
Linear solver converged at step: 16, final residual: 1.73457e-05  Nonlinear convergence: ||u - u_old|| = 0.0149353
Linear solver converged at step: 26, final residual: 4.4267e-08  Nonlinear convergence: ||u - u_old|| = 0.00101631
Linear solver converged at step: 57, final residual: 3.90603e-13  Nonlinear convergence: ||u - u_old|| = 1.21151e-06
 Nonlinear solver converged at step 3


*** Solving time step 9, time = 0.1 ***
Linear solver converged at step: 11, final residual: 0.000222815  Nonlinear convergence: ||u - u_old|| = 0.0505091
Linear solver converged at step: 16, final residual: 1.39453e-05  Nonlinear convergence: ||u - u_old|| = 0.0133655
Linear solver converged at step: 26, final residual: 4.68354e-08  Nonlinear convergence: ||u - u_old|| = 0.000730003
 Nonlinear solver converged at step 2


*** Solving time step 10, time = 0.11 ***
Linear solver converged at step: 10, final residual: 0.000233755  Nonlinear convergence: ||u - u_old|| = 0.0312662
Linear solver converged at step: 16, final residual: 1.53343e-05  Nonlinear convergence: ||u - u_old|| = 0.0114697
Linear solver converged at step: 25, final residual: 4.78201e-08  Nonlinear convergence: ||u - u_old|| = 0.000618281
 Nonlinear solver converged at step 2


*** Solving time step 11, time = 0.12 ***
Linear solver converged at step: 10, final residual: 0.000145843  Nonlinear convergence: ||u - u_old|| = 0.0205185
Linear solver converged at step: 18, final residual: 5.65679e-06  Nonlinear convergence: ||u - u_old|| = 0.00791788
Linear solver converged at step: 27, final residual: 9.42197e-09  Nonlinear convergence: ||u - u_old|| = 9.26946e-05
 Nonlinear solver converged at step 2


*** Solving time step 12, time = 0.13 ***
Linear solver converged at step: 9, final residual: 0.000232166  Nonlinear convergence: ||u - u_old|| = 0.0134885
Linear solver converged at step: 16, final residual: 1.09545e-05  Nonlinear convergence: ||u - u_old|| = 0.00714973
Linear solver converged at step: 22, final residual: 3.6354e-08  Nonlinear convergence: ||u - u_old|| = 0.000139754
 Nonlinear solver converged at step 2


*** Solving time step 13, time = 0.14 ***
Linear solver converged at step: 8, final residual: 0.000251508  Nonlinear convergence: ||u - u_old|| = 0.00867291
Linear solver converged at step: 15, final residual: 1.80725e-05  Nonlinear convergence: ||u - u_old|| = 0.00586875
Linear solver converged at step: 23, final residual: 8.55045e-08  Nonlinear convergence: ||u - u_old|| = 0.000295444
 Nonlinear solver converged at step 2


*** Solving time step 14, time = 0.15 ***
Linear solver converged at step: 7, final residual: 0.000278419  Nonlinear convergence: ||u - u_old|| = 0.00370556
Linear solver converged at step: 14, final residual: 1.8148e-05  Nonlinear convergence: ||u - u_old|| = 0.00335723
Linear solver converged at step: 25, final residual: 1.01115e-07  Nonlinear convergence: ||u - u_old|| = 0.000572797
 Nonlinear solver converged at step 2

 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 09:57:41 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 ------------------------------------------------------------------------------------------------------------
| Systems Example 3 Performance: Alive time=1.08079, Active time=1.02321                                     |
 ------------------------------------------------------------------------------------------------------------
| Event                         nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                          w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|------------------------------------------------------------------------------------------------------------|
|                                                                                                            |
| linear solve                  47         1.0232      0.021770    1.0232      0.021770    100.00   100.00   |
 ------------------------------------------------------------------------------------------------------------
| Totals:                       47         1.0232                                          100.00            |
 ------------------------------------------------------------------------------------------------------------

 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=1.0954, Active time=1.05825                                                     |
 -----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DofMap                                                                                                          |
|   SCALAR_dof_indices()             44400      0.0059      0.000000    0.0059      0.000000    0.56     0.56     |
|   add_neighbors_to_send_list()     1          0.0003      0.000324    0.0004      0.000393    0.03     0.04     |
|   build_sparsity()                 1          0.0045      0.004457    0.0049      0.004935    0.42     0.47     |
|   create_dof_constraints()         1          0.0001      0.000070    0.0001      0.000070    0.01     0.01     |
|   distribute_dofs()                1          0.0003      0.000347    0.0013      0.001346    0.03     0.13     |
|   dof_indices()                    118400     0.0369      0.000000    0.0465      0.000000    3.49     4.39     |
|   prepare_send_list()              2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         1          0.0010      0.000998    0.0010      0.000998    0.09     0.09     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_solution_vector()          15         0.0180      0.001201    0.0270      0.001798    1.70     2.55     |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               15         0.0236      0.001573    0.0236      0.001573    2.23     2.23     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        37600      0.0537      0.000001    0.0537      0.000001    5.07     5.07     |
|   init_shape_functions()           94         0.0004      0.000004    0.0004      0.000004    0.04     0.04     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             37600      0.0277      0.000001    0.0277      0.000001    2.62     2.62     |
|   init_reference_to_physical_map() 94         0.0009      0.000009    0.0009      0.000009    0.08     0.08     |
|                                                                                                                 |
| Mesh                                                                                                            |
|   find_neighbors()                 1          0.0007      0.000665    0.0007      0.000665    0.06     0.06     |
|   renumber_nodes_and_elem()        2          0.0000      0.000015    0.0000      0.000015    0.00     0.00     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         15         0.0001      0.000010    0.0507      0.003381    0.01     4.79     |
|                                                                                                                 |
| MeshTools::Generation                                                                                           |
|   build_cube()                     1          0.0005      0.000529    0.0005      0.000529    0.05     0.05     |
|                                                                                                                 |
| Parallel                                                                                                        |
|   allgather()                      1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition()               1          0.0000      0.000032    0.0000      0.000032    0.00     0.00     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          47         0.4033      0.008582    0.4033      0.008582    38.11    38.11    |
|                                                                                                                 |
| System                                                                                                          |
|   assemble()                       47         0.4802      0.010217    0.6169      0.013126    45.38    58.30    |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            238340     1.0582                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------

 
***************************************************************
* Done Running Example systems_of_equations_ex3:
*   example-opt  
***************************************************************
</pre>
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